Channel sounding is the process of measuring the characteristics of a channel so as to design a communication system that best takes advantage of the determined characteristics of the channel. This is typically done by having a transmitter transmit a signal that is made up of a repeating known training sequence and then processing the signal after it has passed through the channel at a receiver to develop an estimate of the channel characteristics. It is well known in the art that the Cramer-Rao bound is the limit to which channel characteristics may be estimated using linear channel sounding techniques. One method of estimating the channel characteristics is to employ the so-called “least squares method”. Doing so, gives conditions that the training sequence must meet in order to achieve the Cramer-Rao bound.
One condition that, if met, will yield a channel estimate at the Cramer-Rao bound is that the training sequence be orthogonal. However, the art was typically only aware of orthogonal sequences that were very short, e.g., no greater than 16 symbols, or several sequences that were much longer, at lengths of (2n)2, where n in an integer. The use of the known short sequences was of no value, because they cannot be used to measure channels with large delay spread, such as is required for wideband communication. The use of the known long sequences was also of no value, because they require complicated modulation schemes that are not practical to implement. Thus orthogonal sequences were not used in the art and no practical study was devoted to the use of orthogonal sequences for channel sounding.
Instead, so-called “M-sequences”, which are pseudo-orthogonal sequences, have become the pervasive sequences that are employed for channel sounding. These M-sequences have been extensively studied, with much literature being devoted to them and their use in channel sounding. Thus, the entire mindset of the art was to not employ orthogonal sequences, which were dismissed as impractical.
The signals conveyed in data transmission systems generally are not periodic and occupy infinite bandwidth. In order to limit the occupied bandwidth, the transmitted signals are filtered by a channel or pulse shaping filter. Channel filters are also referred to by those of skill in the art as pulse shaping filters.
Because M-sequences are not actually orthogonal, it is common practice in the art to apply a channel filter similar to those applied to data transmission systems when using M-sequences for channel sounding applications. Disadvantageously, this adds to the cost of the system.
As described therein an orthogonal training sequence can be developed for a channel that is described as a finite impulse response (FIR) filter .having a length Mnew from the already existing orthogonal training sequences for at least two channels that have respective lengths Mold1 and Mold2 each that is less than Mnew such that the product of Mold1 and Mold2 is equal to Mnew when Mold1 and Mold2 have no common prime number factor. More specifically, a set of initial existing orthogonal training sequences is found, e.g., using those that were known in the prior art or by performing a computer search over known symbol constellations given a channel of length M. Thereafter, an orthogonal training sequence of length Mnew is developed, where the product of Mold1 and Mold2 is equal to Mnew by repeating the training sequence old1 Mold2 number of times to form a first concatenated sequence and repeating the training sequence old2 Mold1 number of times to form a second concatenated sequence, so that both the first concatenated sequence and the second concatenated sequence have the same length. Each term of the first concatenated sequence is multiplied by the correspondingly located term in the second concatenated sequence which is placed in the same location in a new sequence made up of the resulting Mnew products. This new sequence is an orthogonal sequence of length Mnew. If there is more than one existing orthogonal sequence for a particular length channel, e.g., there may be different orthogonal sequences for different modulation schemes for the same length channel, the implementer may choose which ever orthogonal sequence gives the results desired. Often, for practical applications, the result that yields the modulation scheme that is most suitable for use with the actual channel, which may yield the highest speeds, or the result that yields the smallest alphabet, which would reduce the hardware required for implementation, is desirable.
A popular channel filter that is often used as the channel filter in channel sounding systems that employ M-sequences is the raised cosine filter, a filter that is usually applied in matched pairs, i.e., one at the transmitter and one at the receiver, for various well known technical reasons. In practice these channel filters can only be approximated, and thus the ultimate performance of the communication system is limited.
Channel filtering should not be confused with the reconstruction filtering which takes place when discrete time signals, e.g., digital signals, are converted to continuous time, e.g., analog, signals. The reconstruction filter eliminates the spectral replicas appearing in the continuous time reconstruction of a discrete time signal. The technical requirements placed on the reconstruction filter, e.g., cut off rate and ultimate attenuation can be quite severe. Therefore it is common practice to interpolate the discrete time signal to ease the requirements on the reconstruction filter.
Clearly then, in general, it is the role of the channel filter to define the signal bandwidth while the reconstruction filter assists in the digital to analog conversion process.